Gilles CHANVILLARD, Stéphane RIGAUD

AbstractDuctal is a range of ultra-high performance concrete (UHPFRC), co-operativelydeveloped by BOUYGUES-LAFARGE-RHODIA. Ductal is a technological breakthroughoffering compressive strength of 160 to 240 MPa and tensile strength of over 10 MPa,with true ductile behaviour. Nevertheless, a key question for using ultra-highperformance concrete for building and housing is to have available design codes andcharacterisation methods for such UHPFRC.This paper synthesises the method for a complete characterisation of tensile propertiesof Ductal®. According to the new French Recommendations for UHPFRC, thecharacterisation is done in two steps. The first step deals with the limit ofproportionality or strength to localise the first crack. Taking into account scale effect inflexure, the first-crack strength in direct tension is obtained. The second step deals withthe post-crack resistance. Starting with three points bend tests on notched specimens, aninverse analysis allows to extract the tensile strength versus crack opening relationship.Finally, an analysis of the variability is presented and comparison of the previousapproach with direct tensile tests confirms its validity.

1. Introduction

Ductal is a range of ultra-high performance concrete (UHPFRC), co-operatively

developed by BOUYGUES-LAFARGE-RHODIA. Ductal is a technological breakthroughoffering compressive strength of 160 to 240 MPa and tensile strength of over 10 MPa,with true ductile behaviour. This technology offers the possibility to build structuralelements without passive reinforcements in structural elements and to combineinnovation, lightness, and extreme durability. Nevertheless, a key question for usingultra-high performance concrete for building and housing is to have available designcodes and characterisation methods for such UHPFRC.

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Fax : (33) 4 74 82 80 00 Mail : gilles.chanvillard@pole-technologique.lafarge.comThis crucial issue was addressed by a working group in France over the period 1999 to2002. A guide containing scientific and technical recommendations is now available,meaning that design engineers can now consider the benefits of including metal fibres instructural elements [1]. This guide is divided into three parts. The first focuses on thematerial and the methods of characterising its performance. The second part of thisdocument covers structural element design basis recommendations, identifying the limitstates and normal and shear stresses involved. The third and final part discussesdurability aspects.Our aim in this paper is to fully characterise the tensile mechanical performance of aDuctal® formula, as defined in the French recommendations. We intend to begin bycharacterising the first-crack stress, before looking at post-cracking behaviour. Variousexperimental programmes have been set up to assess all aspects of the material’s tensilebehaviour. We will then establish the relationship between flexural behaviour and directtensile behaviour, which will provide a basis for addressing the notion of scale effect.

2. Description of the Ductal® FM formula

Ductal® concrete has been optimised to satisfy rheological criteria (excellent

workability and self-placing capability), mechanical criteria (very high compressivestrength and non-brittle tensile behaviour) and durability criteria (near-totalinvulnerability to all conventional aggressions). These specifications resulted in somemajor departures from conventional wisdom in the field of concrete formulation.Ductal’s W/C ratio is in the region of 0.2, meaning that a much smaller quantity of wateris needed than that required from a stœchiometric perspective for the cement. The sandused has a fine grading, with the largest grains not exceeding around 600 µm indiameter. The addition of silica fume and optimised use of admixtures are bothabsolutely essential. Last but not least, the concrete is reinforced with metal fibres,which have also been optimised for several criteria. This involved optimising not onlythe behaviour of the individual fibres, but also their interactions within the matrix.A content of 2% by volume of 13-15 mm long fibres with diameters of around 0.2 mmemerged as a good compromise. Calculating the mean spacing of these fibres in thematrix gives a result of around 1.6 mm, which is perfectly compatible with the sandgrading used. Furthermore, we can prove that at a 2% dosage, each fibre has sufficientmobility to satisfy the rheology criterion, without forming clusters, while there is still aspace saturation effect that ensures proper spatial distribution of the fibres throughoutthe volume.

3. Characterisation tests

Before a structural element's design basis can be calculated, we need to identify thematerial's tensile behaviour law. Tests must therefore be conducted to ascertain thistensile performance. The use of direct tensile tests is one avenue, which appears to bethe most direct, although in practice can be very tricky to implement. UHPFRCconcretes release a great deal of energy during crack initiation, and few mechanical

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Fax : (33) 4 74 82 80 00 Mail : gilles.chanvillard@pole-technologique.lafarge.comtesting machines are capable of controlling and monitoring this type of experiment. Inaddition, even with notched specimens, the exceptional performance of these materialsimposes extremely stringent conditions for direct tensile tests (e.g. a good quality bondbetween the specimen and cap, perfect alignment to prevent interference by flexuralstresses, etc.), which make for very long test procedures.

Bending tests are commonly used as a means of evaluating the tensile potential ofconcretes (and other materials). It is widely known that the flexural tensile strength of amaterial does not exactly match its direct tensile strength. However, certain theoreticalmethods involving the scale effect concept make it possible to convert from onestrength to the other. We will come back to this point later.

Thus, for the purposes of the Recommendations and this paper, the tensile behaviour ofDuctal® is characterised primarily using bending tests. We will nevertheless describe theprocedure for validating the analysis of these results with tensile tests.We adopted the following configurations from the French Recommendations :- First-crack stress: four-point bending test on unnotched specimens. This test leads to a constant bending moment in the central area, with no shear force. Consequently, the first crack forms in the weakest part of this area, characterising the dispersion of the material’s first-crack strength.- Post-cracking behaviour: Three-point bending test on a specimen with a notch in the central section measuring 10% of the specimen height. Here, the aim is not to evaluate the first-crack stress, but to characterise the contribution of the fibres as reinforcement of a cracked section. The notch ensures that the fracture occurs in the central area, reproducing the cracking mechanism. Furthermore, as under flexural behaviour UHPFRCC entails severe strain hardening, the three-point bending test on notched specimen reduces the risk of multiple cracking on either side of the central section.It should also be noted that the specimen size must be such that the effects of fibreorientation during manufacture are limited. The Recommendations propose a minimumdimension of five times the length of the fibres, which in the case of Ductal® authorisesthe use of prism-shaped specimens with a 70*70 mm cross-section.

4. Characterising the material’s first-crack strength

The tests were performed on 70*70*280 mm prism-shaped specimens. A device

attached to the specimen enabled the true deflection to be measured (fig. 1). Thedeflection during the test was controlled by a LVDT sensor at a rate of 0.1 mm/min.Using this four-point bending test configuration, it is possible to determine thematerial’s flexural elastic limit or the first-crack stress in flexure. Figure 2 shows aseries of tests conducted on six specimens; in all, three series have been done in order toobtain a good estimate of the mechanical properties, the elastic limit and the modulus ofrupture calculated on the basis of the maximum load.

Figure 1: Deflection measuring device

Figure 2 shows very low dispersion of the material in the linear range, right up to themaximum equivalent stress. Furthermore, this figure clearly reveals the ductile nature ofDuctal in flexion as the first-crack stress is reached at a deflection of around 80 µm,while the maximum effort corresponds to a deflection of 0.9 mm, obtained thanks tofine multiple cracking in the area subject to the greatest moment (photo 1).

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After the peak, the main crack’s location is established and its opening mechanismdepends directly on its tortuosity, location and on how well the fibres are anchored inthe matrix. This accounts for the fact that the softening behaviour varies slightly fromone specimen to another [2].Table 1 synthesises the obtained mechanical properties and shows a very slightvariation of the results along the elastic limit, with an average slightly below 19 MPaand a standard deviation of less than one. However, the values obtained for the modulusof rupture are markedly more dispersed, with standard deviations varying between oneand five. This observation justifies the choice not to use this four-point bending test tocharacterise the post-crack behaviour of UHPFRCC. 9

6 Frequency

0 30 35 36 42 45 50 60 65 Max Sf (MPa)

Figure 3 : Histogram showing the distribution of the modulus of rupture

As the results are distributed according to a gaussian law (fig. 3), and considering thatthe 18 specimens are representative of an infinite population, we can perform a moreprecise statistical analysis in order to calculate the properties that characterise thisDuctal® formula, the elastic limit and the modulus of rupture, with a confidence intervalof 95%. Table 2 summarises this global analysis.

The confidence interval of 95% was calculated on the basis of the standard deviationsobtained and the reverse Student’s law. Thus, the elastic limit can be said with a 95%degree of certainty to lie between 18.5 MPa and 19.1 MPa. Similarly, the maximumequivalent stress is 46.6 MPa ± 2.8 MPa, with a 95% confidence interval. Figure 4shows the mean curve obtained from the 18 four-point bending tests, and illustrates theabove statistical analysis by means of error bars for the elastic limit and modulus ofrupture. 50

5. Characterising the material’s post-crack behaviour

Three-point bending tests were used to characterise post-crack behaviour. These testswere performed on 70*70*280 mm prism specimens with a 10 mm deep notch. Crackopening was controlled by an extensometer attached to the specimen (fig. 5), at a rate of40 µm/min.This type of test can be used to characterise the material' s post-cracking flexuralbehaviour according to the bending moment M in relation to the crack width w at thenotch that determines the crack location. Figure 6 shows the curves obtained from fivespecimens, plus the mean curve.Again, the material's pseudo ductility is put in front. The material exhibits an essentiallyelastoplastic behaviour up to w = 0.5 mm. As already mentioned, these tests do not

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Fax : (33) 4 74 82 80 00 Mail : gilles.chanvillard@pole-technologique.lafarge.comprovide a sound basis for stating a result for the elastic limit, because of the presence ofthe notch.

Figure 6: Three-point bending tests on notched Ductal® specimens

However, one might be surprised at the dispersion of these curves, with a maximumequivalent stress of 32.8 MPa on average with a standard deviation of 3.70, as the verypresence of the notch should limit the width of the curve pattern. Upon examining thespecimens, we noted that in some, between one and three cracks had initiated in thenotch, rather than the single crack theoretically expected. This was probably due to thedepth of the notch, which in view of the material’s significant flexural strain-hardeningcharacteristics, was insufficient to concentrate the stresses in a single section.

6. Direct tensile tests

Tests were performed on 160 mm long prism specimens with a 70*70mm cross-section.An extensometric device consisting in three LVDT displacement sensors was attachedto the specimen, in order to measure the extension, and the testing machine wascontrolled taking the mean readings of these three sensors at a speed of 6 µm/min. The

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6.1 Tests on notched specimens

Two notches were made on opposite sides of the specimen. Such test configurationmakes it possible to localise the cracking area, and then to identify the constitutiveequation relating the tensile stress as a function of crack width. Figure 7 shows theresults obtained, and the mean curve. The stress spikes in each graph reflect thedifficulties controlling the test rate during the sudden release of energy that occurred asthe crack grew.

18

16

14

12 Fib118-1 Stress (MPa)

Fib118-2 10 Fib118-3 Fib118-4 8 Fib118-5 Fib118-6 6 Fib118-moy

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Crack opening (mm)

Figure 7: Direct tensile test on notched Ductal® specimens

We were unable to estimate the material’s elastic limit, for the same reasons as before.Nevertheless, figure 7 clearly shows Ductal’s elastoplastic behaviour up to crackwidths of 0.35 mm. There were also several cracks that began in the notch, and as suchwere responsible for these variations in terms of the maximum stresses reached during

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Fax : (33) 4 74 82 80 00 Mail : gilles.chanvillard@pole-technologique.lafarge.comthe test, i.e. 13.8 MPa to 17 MPa, with the average being 15.1 MPa and a standarddeviation of 1.23 MPa. Such values are very high and due to the very good efficiency ofthe 2% volume content of fibres (photo 2).It is interesting to compare this value with a very simplified approach to the material’smechanical behaviour. The potential tensile strength of a fibre-reinforced concrete canbe calculated using the following formula: S = Sf*Vf*k*gWhere: S is the material’s potential direct tensile strength. Sf is the direct tensile strength of the steel used in the fibres. Ductal® containsfibres with an elastic limit of 2,500 MPa. Vf is the fibre content by volume: 2% in the case of Ductal®. k is a coefficient that takes account of the orientation of the fibres in thematerial. We have assumed a value of 0.6, representing an intermediate fibredistribution between the 2D and 3D cases. For information, the orientation coefficient is0.5, 2/π or 1 for 3D, 2D and 1D distributions, respectively. g is a coefficient that takes account of the effectiveness of the fibre/matrixcombination. With an optimised combination, i.e. one where the fibre is most solicitedwhen perfectly centred relative to the crack, we can assume g=0.5, to allow for the lossof efficiency of straight fibres whose anchored lengths vary from 0 to L/2.

This formula yields a potential strength of 15 MPa, which is totally consistent with ourdirect tensile tests. The fact that this order of magnitude coincides with ourexperimental results supports our view that the fibre/matrix combination used inDuctal® works well.

These results can also be compared with those obtained by a reverse analysis of thebending test results. This method can be applied to the notched specimens’ three-pointbending curves in order to deduce the material’s tensile constitutive equation [3,4]. Theinput parameter for this model is the relationship between the bending moment M andthe crack width w, with the first-crack moment M0 representing a crack width of zero.This model is based on a kinematics assumption of compatibility between a crackedarea where the fibres are active and an uncracked area where the concrete has a linearelastic behaviour [5]. This has been validated on many occasions with fibre-reinforcedconcretes, and has now been included in the French recommendations on UHPFRCs,both in relation to design tools and the methods used to characterise the performance ofthese materials [1].Figure 8 shows the mean curve derived from the direct tensile tests on notchedspecimens, (see individual curves in figure 6) and the tensile behaviour determined byreverse analysis on the mean curve calculated from the results illustrated on figure 5.The experimental results correlate well with the theory. The oscillations in the modelare due to the numerical convergence methods used, and are not representative of themodel. The effect of the notch in the three-point bend tests rapidly disappears, as thereverse analysis coincides with the experimental curve in terms of amplitude. However,the crack widths obtained with the model were slightly overestimated, as sometimes

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Fax : (33) 4 74 82 80 00 Mail : gilles.chanvillard@pole-technologique.lafarge.comseveral cracks initiated in the notch. In such cases, the extensometer (fig. 5) measuredtotal widths, whereas strictly speaking, the model is based on the growth mechanism fora single crack. In practice, this multiple cracking does not affect the order of magnitudeof the stresses estimated using the reverse analysis method, inasmuch as the materialbasically exhibits a perfect plastic behaviour.

16

14

12

10 Stress (MPa)

Experimental curve 8 Reverse analysis

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Crack opening w (mm)

Figure 8: Results of the direct tensile tests and reverse analysis

6.2 Tests on unnotched specimens

Tests were performed on 160 mm long prism-shaped specimens with a 70*70 mmcross-section. The extensometer’s measuring span was 150 mm. Several tests wereperformed, and a typical result is shown in figure 9. This test is very tricky to perform,as it requires an extremely stiff testing machine and advanced servo-control equipment.As the specimens are bonded, we repeatedly encountered bond failure problems at theconcrete-adhesive interface. Any defects liable to generate stress concentrations in theconcrete-adhesive interface are critical inasmuch as the adhesive imparts a direct tensilestrength of around 15 MPa to the concrete-aluminium system.It is interesting to note that the material’s elastic limit is in the region of 11.5 MPa, whenthe average from several tests is calculated. The curve contains breaks of varying sizes,which can be attributed to the test control mechanism. The testing machine had troublemaintaining the setpoint speed of 6 µm/min when a new crack formed, because a largeamount of energy is suddenly released when a crack initiates, the material becomestemporarily unstable and a short time is required for the fibres to take up the load. Eachbreak in the curve represents a new crack; Ductal®’s direct tensile behaviour ischaracterised by multiple cracking and strain-hardening (photo 3).

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Figure 9: Direct tensile test on Ductal® unnotched specimens

Photo 3 : Multiple cracking of Ductal® in pure tensile test

Another important parameter is given by this test : the elastic modulus represented bythe slope of the linear section. Calculating the average over several tests gives therelatively high value of 58,000 MPa.The degree to which the fibres affect the elastic limit can be assessed by using a law ofmixtures to calculate the elastic modulus of the matrix, as the volume and Young’smodulus of the fibres are known, (2% by volume, Ef=210,000 MPa). This simplifiedapproach is possible on the assumption that the material is homogenous and the fibresclose enough together. On the basis of the above results, this calculation yields:- Contribution of the fibres to the Young’s modulus (law of mixtures): 4,200 MPa- Elastic modulus of the matrix only: 5,8000 – 4,200 = 53,800 MPa- Strain at first crack under tensile load: εc = 11.5/58,000 = 1.9.10-4,- Tensile stress taken up by the matrix: Sm = 1.9.10-4*53,800 = 10.6 MPa.

Thus, the fibres contribute approximately 1 MPa, or less than 9%, to the elastic limit.This result is very interesting as il leads to the conclusion that the fibres in Ductal®contribute both at material level (first crack strength) and at the structural level (post-crack strength).

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We have seen that Ductal®’s elastic limit in flexural tension (table 2) is 18.8 MPa,compared with only 11.5 MPa in direct tension. It is the latter value, however, that isused in structural design basis calculations. The reason behind this difference is aphenomenon known as the scale effect. This effect does not exist with perfectly brittlematerials, and is dependent among other things on the specimen’s geometry and thematerial’s damage mechanism. This means that during a bending test, the specimen issubjected to a compressive-tensile stress gradient, and the material is damaged bymicro-cracking ahead of the crack front, in order to reduce the stress concentrations.This fracture area enables load transfer to be maintained and creates the scale effect.Models based on the concept of a cohesive crack seek to model this load transfer in thedamaged area, and are now capable of accurately reproducing what is observedexperimentally. Such models notably introduce an essential mechanical quantity – thecracking energy – which incorporates the material' s ability to dissipate energy as a crackgrows [6]. To allow for this scale effect, the CEB-FIP code [7] uses the followingsimplified formula; the coefficient α depends on the concrete formulation, and variesbetween 1 and 2 depending on the concrete' s brittleness:

In order to determine the value of the α coefficient, we conducted a series of tests on thebasic Ductal® matrix with no fibre reinforcement, using specimens of varying sizes.Table 3 summarises the results obtained, and figure 13 shows the scale effect for an αcoefficient of 2.5. The corresponding direct tensile strength is 10.8 MPa, whichcoincides perfectly with the value obtained by deduction from the direct tensile testsafter taking into account the contribution made by the fibres.

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1.7 CEB formula

experimental datas

scale effect 1.6

1.5

1.4

1.3

1.2 30 40 50 60 70 80 90 100 110 specimen height (mm)

Figure 13 : Comparison of experimental and theoretical scale effect

It may be surprising to see that the α coefficient required in order to correctly define thescale effect on the fibre-less matrix is relatively high. This directly reflects the morebrittle nature of UHPFRCCs compared with standard concretes, on account of the muchmore compact cement paste and the small size of the largest aggregate grades. Applyingthe α coefficient to the tensile and bend test results obtained with the metal fibre-reinforced Ductal® yields 18.8/1.51 = 12.45 MPa, compared to a value of 11.5 MPaobtained experimentally in direct tension. Therefore, in order to faithfully reproduce thescale effect with these two values, an α coefficient value of 2 must be adopted, whichfor a 70 mm high specimen gives: Sf = 1.64*St hence St = 18.8 MPa/1.64 = 11.5 MPa

It can be seen that with the fibre-reinforced material the α coefficient must be reduced.This indicates that the fibres contribute to the scale effect by reducing the material’sbrittleness; the fibres also allow more energy to be dissipated, even during the micro-cracking phase and is totally in accordance with the fact that steel fibres in Ductal®contribute to the first crack strength.

To conclude on scale effect, we have done a lot of bending tests using various specimensize. It appears clearly that the variation of the modulus of rupture depends on the fibreorientation as a main factor and is not subjected to a scale effect.

performance is such that it need no longer be disregarded in structural design basiscalculations. In simple terms, the Ductal®’s behaviour is elastoplastic up to crack widthsof around 300 µm. Despite this, Ductal® is not a brittle material, which can bedemonstrated by bending tests on specimens of various sizes. The contribution of thefibres was revealed in several areas. They significantly improve the first-crack stress

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Fax : (33) 4 74 82 80 00 Mail : gilles.chanvillard@pole-technologique.lafarge.comand provide ductility as cracks open. They also reduce the material’s brittleness byincreasing the scale effect.Lastly, we proved that it was possible to fully characterise the tensile performance ofUHPFRCs by means of three- and four-point bending tests and by using a method basedon the reverse analysis of these materials’ behaviour. We obtained very good correlationwith the results from direct tensile tests, which are more problematic to conduct.The constitutive equation that characterises tensile behaviour is split into two parts, onecovering the stress-strain relationship up to the cracking limit, and the other dealingwith the stress-crack width strain-hardening aspect.There remains some difficulty in using this second part of the curve in structural designbasis calculations. This is because the failure mechanism systematically causes multiplecracking, and although the load balance can still be calculated by considering aparticular cross-section, evaluating structural deflection is trickier. Multiple crackingmust be taken into account. One possible way to go is to convert the crack opening intoequivalent plastic strains. Then such non linear approach can be directly integrated innumerical software [8]. It quickly becomes clear that these multiple cracking materialsactually offer huge ductile potential on a structural scale, comparable, from a designperspective, to that of reinforced concrete structures.